1. Field of the Invention
This invention relates to methods for performing noise density measurements and, more particularly, to measuring spectral noise densities below the noise floor of a measuring instrument.
2. Description of the Related Art
Scientists and engineers typically use spectrum analyzers to perform spectral noise density measurements. Noise is a result of random motion of electrons, which by the central limit theorem leads to a noise signal of Gaussian distribution. The power of a noise signal is a parameter that is typically measured with spectrum analyzers in the form of noise density.
The log scale on spectrum analyzers usually distorts the original nature of a noise power distribution. In a typical case when VBW/RBW=1, the standard deviation of the noise power distribution on a log scale may be approximately 5.56 dB. Using video averaging (ensemble log averaging, as opposed to true power averaging) available in most spectrum analyzers to “fully-average” noise traces typically affects the power noise density distribution in three ways. First, it may reduce the standard deviation of the noise power distribution. For example, if the standard deviation is approximately 5.56 dB and N is the number of points in the noise trace, the standard deviation may be reduced to 5.56/√{square root over (N)}. Second, it may bias the mean by approximately −2.51 dB. Lastly, it may result in the distribution looking Gaussian even on a log scale.
A “fully-averaged” noise trace may be a trace that does not contain significant “dips/fades”. The low-power points (i.e., “dips/fades”), which on a log scale typically appear as −20 dB or −30 dB points relative to the mean, may bias the statistics. As the trace is averaged, the frequency at which the “fades” occur may decrease until they eventually disappear, which is the point when the trace may be considered to be “fully-averaged”. For such a trace, the statistics may be biased; therefore, in one example, the statistics may be corrected by adding 2.51 dB to the mean and dividing the standard deviation by 1.28.
To interpret the returned spectrum analyzer trace (or the mean of the trace points) as a noise density value in dBm/Hz, the measured level at the output of the spectrum analyzer is typically manipulated in the following three ways to represent the input spectral noise density. First, since log processing may cause an under-response to noise of approximately 2.51 dB, 2.51 dB may be added. Second, normalize to a 1 Hz bandwidth by subtracting 10 times the log of the RBW, where the RBW is given in units of Hz. Lastly, compensate for the over-response due to a mismatch between 3 dB bandwidth and noise bandwidth of the spectrum analyzer. For example, in most analog spectrum analyzers having a 4-pole sync filter type, the over-response may be compensated by subtracting 0.52 dB.
Spectrum analyzers, however, have a certain capability beyond which spectral noise density measurement becomes almost impossible. For example, measuring spectral noise densities below the noise floor of the instrument is typically impossible for most spectrum analyzers.